Is there a way to make layers for textures?
Final &amp; Overview:



If you want to have an easy process you should have proper UV Mapping for your object and two textures.

Cuboid texture - It could be anything you want.

Hair texture - Should be painted on transparent background.

When you have both of them you can Mix them trough Inverted Alpha Channel from your Hair texture.

Blend file:



Edit:

To switch between textures in Texture Paint mode go to Slots tab and select desired texture. Always save them after painting and don't forget to save image file (or pack it) in UV Image Editor.